Bayesian Optimization

Description

Bayesian Optimization of Hyperparameters.

Usage

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BayesianOptimization(FUN, bounds, init_grid_dt = NULL, init_points = 0,
  n_iter, acq = "ucb", kappa = 2.576, eps = 0, kernel = list(type =
  "exponential", power = 2), verbose = TRUE, ...)

Arguments

FUN

The function to be maximized. This Function should return a named list with 2 components. The first component "Score" should be the metrics to be maximized, and the second component "Pred" should be the validation/cross-validation prediction for ensembling/stacking.

bounds

A named list of lower and upper bounds for each hyperparameter. The names of the list should be identical to the arguments of FUN. All the sample points in init_grid_dt should be in the range of bounds. Please use "L" suffix to indicate integer hyperparameter.

init_grid_dt

User specified points to sample the target function, should be a data.frame or data.table with identical column names as bounds. User can add one "Value" column at the end, if target function is pre-sampled.

init_points

Number of randomly chosen points to sample the target function before Bayesian Optimization fitting the Gaussian Process.

n_iter

Total number of times the Bayesian Optimization is to repeated.

acq

Acquisition function type to be used. Can be "ucb", "ei" or "poi".

  • ucb GP Upper Confidence Bound

  • ei Expected Improvement

  • poi Probability of Improvement

kappa

tunable parameter kappa of GP Upper Confidence Bound, to balance exploitation against exploration, increasing kappa will make the optimized hyperparameters pursuing exploration.

eps

tunable parameter epsilon of Expected Improvement and Probability of Improvement, to balance exploitation against exploration, increasing epsilon will make the optimized hyperparameters are more spread out across the whole range.

kernel

Kernel (aka correlation function) for the underlying Gaussian Process. This parameter should be a list that specifies the type of correlation function along with the smoothness parameter. Popular choices are square exponential (default) or matern 5/2

verbose

Whether or not to print progress.

...

Other arguments passed on to GP_fit.

Value

a list of Bayesian Optimization result is returned:

  • Best_Par a named vector of the best hyperparameter set found

  • Best_Value the value of metrics achieved by the best hyperparameter set

  • History a data.table of the bayesian optimization history

  • Pred a data.table with validation/cross-validation prediction for each round of bayesian optimization history

References

Jasper Snoek, Hugo Larochelle, Ryan P. Adams (2012) Practical Bayesian Optimization of Machine Learning Algorithms

Examples

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# Example 1: Optimization
## Set Pred = 0, as placeholder
Test_Fun <- function(x) {
  list(Score = exp(-(x - 2)^2) + exp(-(x - 6)^2/10) + 1/ (x^2 + 1),
       Pred = 0)
}
## Set larger init_points and n_iter for better optimization result
OPT_Res <- BayesianOptimization(Test_Fun,
                                bounds = list(x = c(1, 3)),
                                init_points = 2, n_iter = 1,
                                acq = "ucb", kappa = 2.576, eps = 0.0,
                                verbose = TRUE)
## Not run: 
# Example 2: Parameter Tuning
library(xgboost)
data(agaricus.train, package = "xgboost")
dtrain <- xgb.DMatrix(agaricus.train$data,
                      label = agaricus.train$label)
cv_folds <- KFold(agaricus.train$label, nfolds = 5,
                  stratified = TRUE, seed = 0)
xgb_cv_bayes <- function(max.depth, min_child_weight, subsample) {
  cv <- xgb.cv(params = list(booster = "gbtree", eta = 0.01,
                             max_depth = max.depth,
                             min_child_weight = min_child_weight,
                             subsample = subsample, colsample_bytree = 0.3,
                             lambda = 1, alpha = 0,
                             objective = "binary:logistic",
                             eval_metric = "auc"),
               data = dtrain, nround = 100,
               folds = cv_folds, prediction = TRUE, showsd = TRUE,
               early.stop.round = 5, maximize = TRUE, verbose = 0)
  list(Score = cv$dt[, max(test.auc.mean)],
       Pred = cv$pred)
}
OPT_Res <- BayesianOptimization(xgb_cv_bayes,
                                bounds = list(max.depth = c(2L, 6L),
                                              min_child_weight = c(1L, 10L),
                                              subsample = c(0.5, 0.8)),
                                init_grid_dt = NULL, init_points = 10, n_iter = 20,
                                acq = "ucb", kappa = 2.576, eps = 0.0,
                                verbose = TRUE)

## End(Not run)